In Fourier transform profilometry (FTP) an object is illuminated by both ambient (controlled or uncontrolled) lighting and (highly controlled) sinusoidal fringes (fringes can be at multiple spatial frequencies but are in most implementations single-frequency). An image of the illuminated object is captured and then processed.
To obtain a three-dimensional map of the surface, a portion (e.g. either one-dimensional or two-dimensional) of a full spectrum is typically extracted from the captured image. The full spectrum of the captured image includes a modulated sinusoid corresponding to a height (i.e. depth) information of a surface of the object, wherein a contour of the object spreads (i.e. modulates) the spectrum of the sinusoidal fringes from a single bin to a region (i.e. blob) about the central frequency.
Also present in the spectrum of the captured image is a region referred to as a DC-component, which is a spectral information corresponding to the ambient-illuminated image of the object. The DC-component contains a DC bin, wherein DC stands for a direct current that typically represents an average intensity of the captured image. A region of the spectrum containing the DC-component typically overlaps with a region including the modulated sinusoid and therefore, limits the amount of information one can utilize.
The problems inherent to the overlapping regions of the spectrum of the captured image are currently addressed using multiple images and a one-dimensional spectrum processing.
For example, a method for FTP DC-removal has been proposed including a one-dimensional Fourier transform and an acquisition of an additional image of the object without fringes for use as a DC-spectrum to be removed from an image including the fringe (modulated sinusoid) spectrum. (See Chen and Su, Proc. SPIE V. 4231 p. 412, 2000).
An alternative approach requires the use of two cameras. Specifically, one camera captures an image of the object including reflected fringes, while another camera includes a filter to block a wavelength of the fringe illumination to capture only a DC-component and not the modulated-sinusoid. The “two-camera” solution requires significant increase in cost (additional camera, filter, and optics), system complexity (camera synchronization), and alignment (to ensure that the two cameras have precisely the same field-of-view). It may also be necessary to simultaneously illuminate the object with a non-fringed pulse of light of different wavelength than the fringes for motion-freezing and to provide identical illumination, and thus, identical DC-components for the two cameras (again increasing cost, complexity, and alignment).
It is desirable to develop a system and a method for maximizing a precision of Fourier transform profilometry using a single image and a two-dimensional spectrum processing.